PREFACE
Gravity and Magnetic methods are economically viable and rapid geophysical
interpretation tools that can be employed to solve a wide variety of problems in mineral
exploration, regional geophysical mapping and oil prospecting. Interpretation of
anomalies in many cases particularly regional geophysics ends by correlating the
anomalies with surface geology, identifying certain trends and extrapolating them to
poorly mapped regions. A rigorous quantitative interpretation of these anomalies can
provide good results that help in planning further geophysical strategies and in better
understanding the subsurface geology. Inversion techniques application to potential
fields data helps in estimating the causative sources more precisely. Inversion
technique in potential field methods has neither a unique nor a stable solution. By
applying realistic constraints (relevant to the problem), based on local geological
settings, one may arrive at the actual model. As a result, it requires a large variety of
inversion techniques to make it feasible to interpret field data from the large variety of
existing settings. Because of this, there are more publications based on potential field
inversion during last many years (1977 to 1997) in GEOPHYSICAL RESEARCH journals.
This thesis presents inversion techniques application in geophysics, in particular
in gravity and magnetic prospecting. To study inverse problems in gravity and magnetic,
we have chosen Natural Generalised Inverse (GI) technique via Singular Value
Decomposition (SVD) and Marquardt Inversion (MI) schemes. The specific problems
attempted are estimation of model parameters of fault and dyke models in gravity and
magnetic prospecting.
The present work is divided into six chapters. The first chapter presents
definitions of some standard inversion schemes given by earlier workers followed by, a
brief explanation of an inversion problem and its root, the forward problem. Different
inversion problems attempted by different schools are also presented to indicate
different directions of development. In addition, inversion studies in different branches of
science are briefly surveyed. As the main interest is in the application of the chosen
inversion techniques in prospecting, a review of some of the relevant works that
appeared during the past decade is also presented. The plan of work being taken up in
the thesis is detailed in, “Scope of work “. Error estimation details are presented that
include: data and parameter upper bound, relative error, RMS error and artificial error.
In each synthetic and field example these details are worked out and discussed.
The second chapter is devoted to a detailed description of the forward problems
in gravity and magnetic interpretation of fault and dyke models supported by theoretical
examples. The mathematical expressions describing fault and dyke anomalies are
considered. These expressions are usually referred to as models of fault and dyke.
They contain the model parameters, such as depth to the top of the body, width, dip
etc., of the geophysical models. A study on the nature of the theoretical anomaly, with
changes in the different parameters of the selected model, also forms a part of this
chapter.
In the third chapter some essential features of inversion are outlined. Using the
GI technique with SVD, two synthetic examples are analysed. It is observed that, the
numerical experiment with synthetic data works well. The Generalised inverse method
solves a mixed determined problem over the whole region of observations and has both
data and model resolutions intermediate between the two extremes of over and under
determenancies.
The fourth chapter deals with the application of GI technique using field data,
which is essential to test the performance of the selected techniques. Geophysical data
collection and corrections required, before employing the GI technique, are presented in
the first part of this chapter. GI application to the corrected gravity and magnetic field
data sets forms the other part of the chapter. Two land and one offshore gravity field
examples are subjected to GI plus SVD analysis. The results obtained corroborate with
the general observation that in the case of gravity anomaly, the density contrast is the
dominating model parameter. It is seen in the case of magnetic field data analysis,
assuming a dyke model, factor Q (a function of dip of the dyke, field inclination, profile
strike) is the crucial parameter
The fifth chapter presents in the first part, magnetic data interpretation by
Werner deconvolution method, which gives rough estimates of the dyke model. The
second part describes Marquardt iteration process, the initial model for which is
obtained from Werner model studies. Marquardt iteration process yields updated model
in least square sense. Both these methods are explained with application to magnetic
data.
The second part of this chapter comprises a comparison of the GI and Marquardt
inversion schemes and an error analysis of their performance. GI with SVD has
additional features like model and data resolutions (i.e., related vectors in model and
data space respectively) that enable us to explore details of individual parameter
contribution to the geophysical model.
Chapter six deals with application of GI technique to compute magnetic
basement depth from observed magnetic data of Kakinada -Paradip shelf of eastern
continental margin of India. In the present inversion scheme, the topography is equated
to a series of juxtaposing prisms, one below each anomaly point and the depths ZT to
the top are determined. GI is carried out to refine basement depth along the length of a
profile. The same procedure is adapted to all the profiles in an area that enables us to
generate magnetic basement map of the area.
As a case study, magnetic data between Kakinada (south of Visakhapatnam 17°
41' N, 83° 17' E) and Paradip (20°16' N, 86°42' E), collected - the author is one of the
participants in data acquisition cruise - across the continental margin along 40 coast
normal profiles (at 10 km interval) are taken to generate magnetic basement map using
GI method. In general the basement depth ranges between 2 to 7Km in this off shore
region. In the inner shelf off Chilka Lake, shallow basement (< 1km) is inferred
corresponding to high amplitude magnetic anomalies of the order of 1800 nT. In the
deeper water regions, the basement depth varies from 5 to 7 Km.
The significant features from basement map include a) a shallow and highly
faulted basement, in the inner shelf, (b) a NE-SW ridge and trough configuration in the
mid shelf, c) NW-SE trending basement, off Bhimilipatnam to Kalingapatnam and finally
d) N-S trending shallow basement off chilka Lake. From overall analysis, the basement
configuration derived form GI technique correlate well with earlier results from
conventional methods.
FORTRAN 77 codes employed in the numerical computations are also included.